Devising a deconstructable 2X4 self-standing frame with carriage bolts should be straightforward.
I recommend using the sheet foam insulation as a backer. I mount it to the wood with drywall screws using the plastic discs that come on some type of nail made for holding such things (available at Lowes/Home Depot). You can attach targets to it VERY easily using toothpicks. And it lasts forever. My range sees a considerable amount of action, and in 3 years I've only replaced the backers once. The MLs and shotguns do a number on them, if you shoot 30cal and below they can take hundreds of rounds if you move the targets around a little.